**Yes**.

"*Within range of the illusion*" refers to the 20 ft cube illusionary object or creature, NOT the 120 ft casting radius.

As long as you are within the original casting radius of the illusionary object, you may move it to any other point within range. This lets illusionists keep one persistent Major Image for any amount of time if they can keep using actions to keep it near them.

What defines "*any other point within range*" however, is up to discussion. It could mean you may move the object either 120 ft within the caster, or 120 ft within the illusionary object.